COVID-19 and the Danger of Exponential Growth

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The normally congested freeways of the Bay Area.

On March 6, 2020, Stanford University announced that all classes would be conducted online for the remainder of winter quarter when one faculty member was among 20 confirmed cases of COVID-19 virus in Santa Clara County. On March 17, 2020, Santa Clara County, with 175 confirmed COVID-19 cases, ordered an unprecedented “shelter-in-place” for all residents, together with six other Bay Area counties.

With a rapid rise in confirmed cases, Italy, Spain, and France entered nationwide lockdown in order to slow down the spread of the virus. This caused widespread shortages of personal goods, hygiene products, and groceries for daily lives. Both the governments and civilians were, and still are, caught unprepared.

This rapid rise in case count is the result of exponential growth. For example, if one person contracted with COVID-19 transfers the virus to three other people and each of those three transfers it to another three people, after transmitting ten times, the total number of infected people will be more than 88,000. However, if each infected person only transfers the virus to two people, the total number infected will be only about 2,000 people after ten iterations. Furthermore, if each infected person only transfers the virus to one other person, the total number of infected people will be only 11 people after ten iterations. This shows how dire the situation can be if the virus transmission rate is not controlled.

The seven to 14 day incubation period of COVID-19 makes it difficult for people and government officials to predict the spread of the disease. The current confirmed case count only represents the number of people who have developed severe symptoms and does not count all of the people who may be carrying and transmitting the virus during the initial asymptomatic stage. Any action taken will have a delayed effect on the case count. By that time, the number would have grown exponentially.

The graph below shows the confirmed COVID-19 cases in selected countries after 100 confirmed cases based on data published by Johns Hopkins University as of March 19, 2020 [1].

Most of the countries that did not take aggressive actions to contain COVID-19 have case counts growing at a rate of doubling in less than three days. Even after Chinese and South Korean governments took aggressive actions, this exponential growth curve still continued for more than seven days before the curve started to flatten out.

At the onset of the outbreak, the Chinese government enforced a strict lockdown in Hubei Province and many other regions in the country. There the daily new confirmed case is finally coming down to single digit or even zero from a peak of a few thousands after two months of lockdown [1][2]. South Korea took a different approach. Instead of imposing a massive lockdown, the government only implemented a lockdown in the most concentrated region. On the other hand, the government quickly ramped up virus testing capacity to massively screen the population for infected people. The infected people were isolated and treated early to prevent virus spread and to reduce the death rate [3]. Because the South Korean government acted quickly, particularly with extensive testing, the case count has saturated to a level one order of magnitude lower than that in China.

It is interesting to note that Japan, Singapore, and Hong Kong have relatively mild case growth rates in which cases double in eight to 15 days despite the close proximity that these countries/regions have to the epicenter, China. This is probably because the governments and citizens in Singapore and Hong Kong have learned hard lessons from the SARS (Severe Acute Respiratory Syndrome) outbreak in 2003. When the COVID-19 outbreak erupted in China, both Hong Kong and Singapore governments immediately put travel restrictions on mainland China. Hong Kong canceled school immediately after the first confirmed case and encouraged social distancing without resorting to a full lockdown. The Singapore government implemented widespread testing to quickly identify and isolate the infected people to prevent the virus spread [4].

In contrast, the western world did not put in travel restrictions nor enforce social distancing in the early stage. The countries started to shut down schools and implement massive lockdowns at a much later stage when the confirmed case counts reached high thousands. If the case count continues to grow exponentially for seven to 14 days after the lockdown, the case count can still reach 100,000 or more. If the lockdowns are not implemented, the case count can reach even higher levels.
For infectious diseases with high transmission rate, it is important to keep in mind that the power and danger of exponential growth can cause massive outbreaks if actions are not taken quickly.

Reference:
[1] “Coronavirus COVID-19 Global Cases by the Center for Systems Science and Engineering (CSSE) at Johns Hopkins University (JHU).” John Hopkins, 19 Mar. 2020, coronavirus.jhu.edu/map.html.
[2] Cyranoski, David. “What China’s coronavirus response can teach the rest of the world.” Nature, Mar. 17, 2020, www.nature.com/articles/d41586-020-00741-x.
[3] Terhune, Chad et al. “Special Report: How Korea trounced U.S. in race to test people for coronavirus,” Reuters, 18 Mar. 2020, www.reuters.com/article/us-health-coronavirus-testing-specialrep/special-report-how-korea-trounced-u-s-in-race-to-test-people-for-coronavirus-idUSKBN2153BW.
[4] Asquith, James. “Coronavirus containment – what we can learn from relative calm in Singapore and Hong Kong.” Forbes, Mar. 16, 2020, www.forbes.com/sites/jamesasquith/2020/03/16/coronavirus-containment-what-we-can-learn-from-relative-calm-in-singapore-and-hong-kong/#c4231cd1040e.